We consider different models that assess eco-efficiency in the perspective of production frontier estimation. These models span from the ones that consider bad outputs as inputs, or as outputs under the weak disposability assumption, or under the weak G-disposability and the materials balance principles, or under the modeling of multiple sub-technologies like the by-production model, or under the natural and managerial disposability concepts. These models are confronted to livestock farming data (meat sheep) and greenhouse gas pollution in French grassland areas, to discuss their suitability in eco-efficiency measurement. A major contribution is that we propose a new version of the by-production approach by augmenting it with ‘interdependence constraints’. Although all models considered here confirm the existence of large improvement potentials, all except the by-production model converge to the same results as in the case where undesirable outputs are treated as inputs. By contrast, the by-production model with interdependence provides more realistic results than the other models.